Dell Inc. has agreed to sell itself to founder and CEO Michael Dell and Silver Lake for $24.4 billion, or $13.65 per share.

But Southeastern, Dell's biggest independent shareholder, and Icahn teamed in May to pitch an alternative plan that would let Dell shareholders keep their stake in the company and give them either $12 per share in cash or additional shares.

In a Securities and Exchange Commission filing Thursday, the pair urged shareholders to vote against the company's proposals at a special meeting July 18. The filing didn't contain any details about their own plan.